Nisse's home page

 Mounir Nisse

  E-Mail: mounir (dot) nisse (at) gmail (dot) com, 

mounir (dot) nisse (at) xmu (dot) edu (dot) my,

 nisse (at) ihes (dot) fr

The primary focus of my research  lies in the areas of complex algebraic geometry,  computational algebraic geometry,  tropical geometry, complex analysis,  combinatorics, deformation of singularities,  and (co)amoebas  of complex varieties. Right now I am an Associate Professor at Xiamen University Malaysia. Before that, I was an  invited Researcher at IHES, Bures-sur-Yvette, France. Previously, I was Postdoctoral Fellow  at MSRI - Berkeley, CA in fall 2009. Prior to that, I was  a  Visiting  Assistant Professor  at Texas A&M University, College Station 2010-2013,    and a  Guest Researcher at  Max Planck Institute for Mathematics  in Bonn, Germany June-December 2013,  and then an Assistant Professor of mathematics at  School of Mathematics, Korea Institute for Advanced Study (KIAS), 2014- 2018.

Geometric and combinatorial structure  of hypersurface coamoebas

For more information,  see the links above.

Published papers:

19 -- Black Hole Thermodynamic Free Energy as A-discriminants, (With Yen-Kheng Lim and Linus Chang), International Journal of Theoretical Physics (2024) 63:176.

18 -- Observing algebraic variety of Lee-Yang zeros in asymmetrical systems via a quantum probe, (with Arijit Chatterjee, T. S. Mahesh and Yen-Kheng Lim), Physical Review A 109, 062601 (2024).  

17 -- Light-ring pairs from A-discriminantal varieties, (with Yen-Kheng Lim), Physical Review D, 104 (2021) 10, 104012.

16 -- Describing Amoebas, (with Frank Sottile),  Pacific Journal of Math. Vol 317  (2022), No 1, pp. 187--205.

15 -- The zero-temperature limit of grand canonical ensembles via tropical geometry, (with Yen-Kheng Lim), J. Analysis and Mathematical Physics, (2021), https://doi.org/10.1007/s13324-021-00555-8

14 -- A natural topological manifold structure of phase tropical hypersurfaces, (With Y. R. Kim),  J. Korean Math. Soc. 58 (2021), No. 2, pp. 451--471.

13 -- Amoeba-shaped polyhedral complex of an algebraic hypersurface, (with Timur Sadykov),  Journal of Geometric Analysis, Vol.  29, Issue 2, (2019), pp. 1356-1368.

12 -- Metric Estimates for Archimedean Amoebae and Tropical Hypersurfaces, (with M. Avendano, R. Kogan, and J. M. Rojas), Journal of Complexity, Vol. 46, June 2018, pp. 45-65.

11 -- Amoeba basis of zero-dimensional varieties, J. Pure Appl. Algebra 220, no 3, (2016), 1252-1257.

10 -- Higher convexity for complements of tropical varieties, (with F. Sottile), Math. Annalen, Vol. 365, Issue 1, (2016), 1–12.

9 -- Higher convexity of coamoeba complements, (with F. Sottile), Bull. London Math. Soc. Vol. 47, no 5, (2015), 853-865.

8 -- Amoebas and coamoebas of linear spaces, (with M. Passare), Analysis Meets Geometry: A Tribute to Mikael Passare. Editors: M. Anderson, J. Boman, C. Kiselman, P. Kurasov and R. Sigurdsson, Trends in Mathematics, 63–80, Springer/Birkhuser AG 2017.

7 -- Analytic varieties with finite volume amoebas are algebraic, (with F. Madani), J. Reine Angew. Math., Vol. 706, (2015), 67–81.

6 -- Non-Archimedean coamoebae, (with F. Sottile), Contemporary Mathematics Amer. Math. Soc. Vol. 605, (2013), 73–91.

5 -- Generalized logarithmic Gauss map and its relation to (co)amoebas,  (with F. Madani), Math. Nachr. 286, No. 14–15, (2013), 1510–1513.

4 -- On the volume of complex amoebas, (with F. Madani). Proc. Amer. Math. Soc., 141, (2013), 1113–1123.

3 -- The phase limit set of a variety, (with F. Sottile), Algebra & Number Theory, 7-2, (2013), 339–352

2 -- Complex tropical localization, and coamoebas of complex algebraic  hypersurfaces, Contemporary Mathematics Amer. Math. Soc., Vol. 556, (2011), pp. 127– 144.

1 -- On the geometry of coamoebas of complex algebraic hypersurfaces. Oberwolfach Report, vol. 6, issue 1, 56-59, (2009).

 Submitted papers and preprints:

20 -- New subexponential fewnomial hypersurface bounds, (with Jens Forsgard and Maurice J. Rojas), submitted for publication, arXiv:1710.00481.

21 -- A tropical characterization of complex analytic varieties to be algebraic, (with Farid Madani, and Lamine Nisse), Preprint arXiv:1407.6459, submitted for publication.

Papers in preparation:

22 -- Phase tropical varieties, in progress.

23 -- Topological description of complex and phase tropical hyperplanes via amoebas, in progress.

24 -- The higher order map and higher solidity for amoebas, (with F. Sottile and Avgust K. Tsikh), in progress.

25 -- Discriminant coamoebae in dimension three, (with F. Sottile and J. Forsard), in progress.

26 -- Dimer models in the torus in higher dimensions, in progress.

27 -- Phases of cycles in the complements of higher codimension amoeba according to Okounkov, in progress.

28-- On the number of complement components of algebraic hypersurface

coamoebas, in progress.

29 -- On the bound of amoebas volume and its sharpness, (with F. Madani), in progress.

Preprints:

30 -- Amoeba basis does exist in general, preprint, preprint, arXiv:1403.3912, (2014).

31-- Geometric and Combinatorial Structure of Hypersurface Coamoebas. Preprint, arXiv:0906.2729 (2009).

32 -- Coamoebas of complex algebraic plane curves and the logarithmic Gauss map. Preprint, arXiv:0805.2872, (2008).

33 -- Maximally Sparse Polynomials have Solid Amoebas. Preprint, arXiv:0704.2216, (2007).

34 -- Sur la connexité du schéma de Hilbert H3,g, preprint (2005).